Which of the following is an equation of a circle that's inscribed in the square?

Question

In the standard xy coordinate plane, the vertices of a square have coordinates (0,4), (4,4), (4,0), and (0,0). Which of the following is an equation of a circle that's inscribed in the square?

 

A . (x+2)²+(y+2)²=2

B. (x-2)²+(y-2)²=2

C. (x-2)²+(y-2)²=4

D. (x+2)²+(y-2)²=4

E. (x+2)²+(y+2)²=8

Answer 1

Draw the square on an xy coordinate system labeling the vertices.  A circle inscribed inside the square will touch each edge of the square.  Draw the circle inside the square.  First find the center of the square which is the midpoint of a diagonal.  This point will also be the center of the circle.

 

Using (0,0) and (4,4) we have ((0+4)/2, (0+4)/2) = (2,2).

 

Find the radius of the circle by noting that the radius is one-half the length of a side.  Find the length of a side using the distance formula and divide by 2.  Using (0,0) and (4,0) we have

 

d = sqrt( (4-0)² + (0-0)²) = 4 → r = 4/2 = 2

 

Now use the standard equation for a circle with center (2,2) and radius = 2

 

(x - 2)² + (y - 2)² = 2²

Answer 2

The formula for a circle is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.  If a circle is inscribed in a square, then its diameter is the same as the side length of the square.

 

I think that should be enough to get you on the right road. :-)